Another poster a few weeks ago gave a nice tip, which does work within the same drawing.
1. Make the viewport you wish to copy, into a block temporarily. Do not worry if it "blinks out".
2. Copyclip it and paste it into the target layout tab.
3. Now explode it and it should retain its layer freezes. If it is turned off, then turn it on.
4. Go back and explode the original and it should restore to its pre-block state.